- #1

ZedCar

- 354

- 1

## Homework Statement

The one-dimensional heat diffusion equation is given by :

∂t(x,t)/∂t = α[∂^2T(x,t) / ∂x^2]

where α is positive.

Is the following a possible solution? Assume that the constants a and b can take any positive value.

T(x,t) = exp(at)cos(bx)

## Homework Equations

## The Attempt at a Solution

T(x,t) = exp(at)cos(bx)

∂T/∂t = a exp(at) cos(bx)

∂^2 T/∂x^2 = -b^2 exp(at) cos(bx)

As a, b and α are all positive this cannot be a solution.

A friend and I were working on this and got the answer above. Though as it was about a week ago I can't exactly remember what we've done here.

In the first step I think we've differentiated exp(at) with respect to t, treating the cos(bx) as a constant multiplier, which become a exp(at) cos(bx).

Is that all correct above?

Then we differentiated again with respect to t.

So wouldn't that become;

∂^2 T/∂x^2 = a^2 exp(at) cos(bx)

Why did we previously get ∂^2 T/∂x^2 = -b^2 exp(at) cos(bx)

Thanks!